In my talk I will discuss some remarkable correspondence between symplectic varieties and vertex algebras, which has been discovered by physicists in the study of the four-dimensional N = 2 superconformal field theories. In the special class of the four-dimensional N = 2 superconformal field theories called the “theory of class S”, such correspondence is mathematically explained in terms of the two-dimensional topological field theories, that involves the Moore-Tachikawa conjecture on symplectic varieties that has been recently proved by Braverman, Finkelberg and Nakajima, and its upgrade to the setting of vertex algebras.